Yeah, nausia and diarrhea/loose stools can really run you dry at a vet. It's rough because it can cause the animal to become dehydrated--which can really worsen any underlying illnesses and even make the animal very sick very quickly, so vets want to work fast and unfortunately there are so many possible causes that they just have to run tests to figure it out, and then they would want to give medication to help settle the stomach to prevent dehydration and just get the cat feeling better.
Not to mention, most cats are experts at hiding their illnesses. We often don't see a cat in at the vet until some problem had been persisting for months without the owners really noticing. When a cat shows extreme signs of illness, it often means they are so sick they can't even focus on hiding from predators, which is not a good sign. It can also mean the owner is observant or the cat is less likely to hide illnesses because of their personality, but that's hard to know unless you have a personal vet who sees your cat often and knows him well. Otherwise it's scary to see a very ill cat.
There could be a foreign body in his stomach--see if any fibers are in his stools, maybe he ate something that is causing irritation. If he ate any old food off the floor it could have disrupted his digestive process as well, which could cause the diarrhea. They might ask to do x-rays if they suspected something like that, which of course would cost you.
There could also be intestinal parasites as you mentioned, but if it was that bad you'd likely see your cats belly to feel swollen and distended(hard, like full of gas feeling)
Some vets would also want to try a giardia test to see if there is an infection in there. Some vets might even want to run blood work to see if there is some kind of organ failure.
It's a difficult thing to be honest--It's hard to find a balance to make everyone happy. On the one hand, if the vet were to not offer these treatments and the cat were to pass away, that would just be awful and would be on everyone's hearts. But on the other hand if there is nothing wrong and the cat gets better in a day anyway and you cost the owners all that money that could have been saved for an actual emergency, that's also terrible. Most vets like to weigh on the safe side of making sure everything is fine and offering tests, allowing the owners to decline them if they wish, but it's still a rough thing.
Just make sure he continues to drink plenty of water if his stools are loose, keep him hydrated. Keep an eye out for bloody stools as well, and if they start looking weird, take a fecal sample to the vet. Fecals themselves tend to run 15-30 dollars depending on what the vet uses, but if you say everything else is still normal you can wait on that for now.
Another option would be to monitor how much he is eating. Animals who over eat tend to sometimes upset their own stomachs and end up with loose stools.
And cats who aren't feeling well often don't want to use their litter boxes--same thing happens with UTIs or even cats with undiagnosed diabetes.
He's most likely fine, but things can take a turn for the worst very quickly when it comes to things like this. I would wait until you see any other signs before heading out. Expect to need to test a few things, treating for giardia is different than treating for parasites, so you want to make sure you know what the problem is before you get medication. Wait a few days, make sure he drinks water, keep the litter box clean. Maybe for now you can buy some puppy pads to put around the litter box to help catch the stools he's leaving outside the litterbox, then just pick the pads up and throw them away. Keeps the house a bit cleaner at least. Good luck with the kitty!